Why is the Priesthood important?
The Priesthood is important because it is the authority required to perform saving ordinances that are required for exaltation, such as baptism. We know ordinances such as baptism are required for salvation because Jesus taught that we must be baptized to enter into the kingdom of God (see John 3:3-5). Remember, Jesus did not just go to anyone to be baptized, he sought out John because he had the Priesthood authority to baptize. Even Jesus had to be baptized because it is a commandment for all of us (see 2 Nephi 31:5), and so he needed to be baptized by the proper priesthood authority.
How is this Priesthood authority obtained?
While many people think that studying theology is enough to claim devine authority, the Bible teaches the exact opposite. In Hebrews 5:4 we read, "And no man taketh this honour unto himself, but he that is called of God, as was Aaron." Ok, so we have to be called of God the way Aaron was; we don't take it upon ourselves, so how was Aaron called? We can read about how Aaron was called of God in the Old Testament:
Called of God, as was Aaron
Aaron was called to receive the Priesthood through one of God's servants who also had the Priesthood, in this case Moses, the prophet at that time. God said to Moses in Exodus 28:1: "And take thou unto thee Aaron thy brother, and his sons with him, from among the children of Israel, that he may minister unto me in the priest’s office, even Aaron, Nadab and Abihu, Eleazar and Ithamar, Aaron’s sons." The event is also recorded in Exodus 30:30 where the Lord tells Moses, "And thou shalt anoint Aaron and his sons, and consecrate them, that they may minister unto me in the priest’s office."
How is the Priesthood given/received?
The Priesthood is given and received by the laying on of hands by someone who has the Priesthood authority. There are many examples of this throughout the scriptures and I will share a three here:
(1) Moses gave Joshua the priesthood by the laying on of hands in Numbers 27:18, "And the Lord said unto Moses, Take thee Joshua the son of Nun, a man in whom is the spirit, and lay thine hand upon him" - feel free to click the link and read the full context if you are unfamiliar with the story.
(2) When the Apostles met together to call new Apostles and give them authority, they also laid their hands upon them:
5 And the saying pleased the whole multitude: and they chose Stephen, a man full of faith and of the Holy Ghost, and Philip, and Prochorus, and Nicanor, and Timon, and Parmenas, and Nicolas a proselyte of Antioch:(3) Paul reminds Timothy of how he was given the Priesthood ordination by the laying on of hands in 1 Timothy 4:14, "Neglect not the gift that is in thee, which was given thee by prophecy, with the laying on of the hands of the presbytery."
6 Whom they set before the apostles: and when they had prayed, they laid their hands on them. (see Acts 6:6)
Recap: How do we get the priesthood?
We must (1) be called of God by one of his chosen servants and (2) receive the Priesthood from someone else who has the Priesthood, by the laying on of hands.
Painting depicting how the priesthood was conferred by Christ as recorded in the New Testament: